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The Alternating Group of Degree 6 in the Geometry of the Leech Lattice and K 3 Surfaces
Author(s) -
Keum JongHae,
Oguiso Keiji,
Zhang DeQi
Publication year - 2005
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611504014984
Subject(s) - mathematics , simple group , geometry , group of lie type , lattice (music) , finite geometry , sporadic group , pentagon , alternating group , simple (philosophy) , group (periodic table) , degree (music) , pure mathematics , combinatorics , group theory , symmetric group , physics , quantum mechanics , philosophy , epistemology , projective plane , correlation , acoustics
The alternating group of degree 6 is located at the junction of three series of simple non‐commutative groups: simple sporadic groups, alternating groups and simple groups of Lie type. It plays a very special role in the theory of finite groups. We shall study its new roles both in a finite geometry of a certain pentagon in the Leech lattice and also in the complex algebraic geometry of K3 surfaces. 2000 Mathematics Subject Classification 14J28, 11H06, 20D06, 20D08.